Uniqueness of the Fock representation of the Gowdy $S^1\times S^2$ and $S^3$ models

Abstract

After a suitable gauge fixing, the local gravitational degrees of freedom of the Gowdy $S^1\times S^2$ and $S^3$ cosmologies are encoded in an axisymmetric field on the sphere $S^2$. Recently, it has been shown that a standard field parametrization of these reduced models admits no Fock quantization with a unitary dynamics. This lack of unitarity is surpassed by a convenient redefinition of the field and the choice of an adequate complex structure. The result is a Fock quantization where both the dynamics and the SO(3)-symmetries of the field equations are unitarily implemented. The present work proves that this Fock representation is in fact unique inasmuch as, up to equivalence, there exists no other possible choice of SO(3)-invariant complex structure leading to a unitary implementation of the time evolution.

10 pages, minor changes, version accepted for publication in Classical and Quantum Gravity

References in corpus (5)

• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Quantum Gowdy $T^3$ model: A uniqueness result
• Quantum Gowdy $T^3$ model: A unitary description
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• Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
• Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
• A Brief Overview of Results about Uniqueness of the Quantization in Cosmology
• Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology
• Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields